
where, \(A\)  is a symmetric positive semidefinite matrix. To study this case we need to add additional constraint to restrict our model to quadratic functions. The following necessary condition for \(f\)  to be a quadratic function can be verified easily, and has been used in SDP performance analysis by Drori et al [1]}:
\(\tfrac{1}{2}\langle \nabla f(x)-\nabla f(y),x-y\rangle =f(x)-f(y)-\langle \nabla f(y),x-y\rangle .\) 
